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Long-Term Stability of the HR 8799 Planetary System Without Resonant Lock

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Long-Term Stability of the HR 8799 Planetary System Without Resonant Lock UvA-DARE (Digital Academic Repository) Long-term stability of the HR 8799 planetary system without resonant lock Götberg, Y.; Davies, M.B.; Mustill, A.J.; Johansen, A.; Church, R.P. DOI 10.1051/0004-6361/201526309 Publication date 2016 Document Version Final published version Published in Astronomy & Astrophysics Link to publication Citation for published version (APA): Götberg, Y., Davies, M. B., Mustill, A. J., Johansen, A., & Church, R. P. (2016). Long-term stability of the HR 8799 planetary system without resonant lock. Astronomy & Astrophysics, 592, [A147]. https://doi.org/10.1051/0004-6361/201526309 General rights It is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), other than for strictly personal, individual use, unless the work is under an open content license (like Creative Commons). Disclaimer/Complaints regulations If you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library: https://uba.uva.nl/en/contact, or a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible. UvA-DARE is a service provided by the library of the University of Amsterdam (https://dare.uva.nl) Download date:28 Sep 2021 A&A 592, A147 (2016) DOI: 10.1051/0004-6361/201526309 Astronomy c ESO 2016 & Astrophysics Long-term stability of the HR 8799 planetary system without resonant lock Ylva Götberg1;2, Melvyn B. Davies1, Alexander J. Mustill1, Anders Johansen1, and Ross P. Church1 1 Lund Observatory, Department of Astronomy and Theoretical Physics, Lund University, Box 43, 22100 Lund, Sweden e-mail: [email protected] 2 Anton Pannekoek Institute for Astronomy, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands Received 14 April 2015 / Accepted 7 June 2016 ABSTRACT HR 8799 is a star accompanied by four massive planets on wide orbits. The observed planetary configuration has been shown to be unstable on a timescale much shorter than the estimated age of the system ( 30 Myr) unless the planets are locked into mean motion resonances. This condition is characterised by small-amplitude libration of∼ one or more resonant angles that stabilise the system by preventing close encounters. We simulate planetary systems similar to the HR 8799 planetary system, exploring the parameter space in separation between the orbits, planetary masses and distance from the Sun to the star. We find systems that look like HR 8799 and remain stable for longer than the estimated age of HR 8799. None of our systems are forced into resonances. We find, with nominal masses (Mb = 5 MJup and Mc;d;e = 7 MJup) and in a narrow range of orbit separations, that 5 of 100 systems match the observations and lifetime. Considering a broad range of orbit separations, we find 12 of 900 similar systems. The systems survive significantly longer because of their slightly increased initial orbit separations compared to assuming circular orbits from the observed positions. A small increase in separation leads to a significant increase in survival time. The low eccentricity the orbits develop from gravitational interaction is enough for the planets to match the observations. With lower masses, but still comfortably within the estimated planet mass uncertainty, we find 18 of 100 matching and long-lived systems in a narrow orbital separation range. In the broad separation range, we find 82 of 900 matching systems. Our results imply that the planets in the HR 8799 system do not have to be in strong mean motion resonances. We also investigate the future of wide-orbit planetary systems using our HR 8799 analogues. We find that 80% of the systems have two planets left after strong planet-planet scattering and these are on eccentric orbits with semi-major axes of a1 10 AU and a2 30 1000 AU. We speculate that other wide-orbit planetary systems, such as AB Pic and HD 106906, are the remnants∼ of HR 8799 analogues∼ − that underwent close encounters and dynamical instability. Key words. planets and satellites: dynamical evolution and stability 1. Introduction an age of >100 Myr is assumed. In this paper we consider HR 8799 bcde∼ as planets; the case of brown dwarfs is more HR 8799 (also called HD 218396 and HIP 114189) is a nearby +20 closely investigated by Moro-Martín et al.(2010). We assume (39:4 1:1 pc; van Leeuwen 2007), young (30 10 Myr assuming ± − the age 30 Myr in this paper as it is estimated from the Columba member of the Columba association; Marois et al. 2010) A5V association. An age of 30 Myr leads to multi-Jovian masses that, (up to F0V) star with mass 1:5 0:3 M (Gray & Kaye 1999; ± however, are still in the planetary regime. Whether it is true that Gray et al. 2003). HR 8799 has four confirmed, directly imaged HR 8799 is associated with the Columba association could be re- planets (Marois et al. 2008, 2010) and a debris disk (Su et al. vealed by Gaia in the near future (Perryman et al. 2001). Other 2009; Matthews et al. 2014). The planet masses are estimated to uncertainties in system properties include distance (39:4 1:1 pc, be 5 (b) and 7 (cde) MJup (Marois et al. 2010). The on-sky sep- van Leeuwen 2007) and stellar mass (1:5 0:3 M , Gray± & Kaye arations between planets and star are estimated to be 67.9 (b), 1999; Gray et al. 2003). ± 38.0 (c), 24.5 (d), and 14.5 (e) AU. Matthews et al.(2014) es- timated the inclination of the system with respect to the plane The formation of the massive HR 8799 bcde planets can be of the sky to be 26 3◦ by observing the outer part of the de- explained by the recently developed models of pebble accretion bris disk and assuming± coplanarity with the planetary orbits. (Lambrechts & Johansen 2012), but the dynamics of the system They estimate the position angle of the inclination to be 64 3◦ has been a puzzle unless resonances are considered. The orbits (G. Kennedy, private communication). Figure1 shows all obser-± of the HR 8799 bcde planets are difficult to constrain as the plan- vations of the planets published at the time of writing. ets have been observed during a small fraction of their orbits (see The estimates of the planetary masses in the HR 8799 sys- Fig.1). In recent work by Pueyo et al.(2015), however, fits are tem depend on the age of the system through cooling models, made to constrain the orbital elements and a variety of solutions indicating higher planet masses with higher age (Baraffe et al. are found, favouring a slightly more eccentric orbit for planet d. 2003). The age of the HR 8799 system is uncertain and has been It is reasonable to believe that the planet orbits are close to circu- estimated using different techniques to range between 30 Myr lar, as with high eccentricity the orbits are likely to cross. How- and 1 Gyr (see Marois et al. 2010, 2008, and references therein). ever, the HR 8799 planetary system appears to be unstable on The planet mass estimates reach the brown dwarf regime when a timescale much shorter than the estimated age of the system Article published by EDP Sciences A147, page 1 of 14 A&A 592, A147 (2016) 2 2. Simulations 2.1. Orbital parameters 1:5 All planets in all our simulations are analogues of the b 1 Pos. angle HR 8799 bcde planets and they are initiated on circular, helio- 64◦ ± 3◦ c centric orbits. The initial orbit inclination we find by drawing a 0:5 random inclination between 0◦ and 5◦ and random longitude of ascending node between 0 and 360◦ (β = 5◦; see Johansen et al. 2012). The initial planet position on the orbit (true anomaly) is 0 e randomised. We assign the mass 1:5 M to the star and the plan- North ["] ets are given the estimated values of the masses, 5 MJup (b) and −0:5 d 7 MJup (cde) if nothing else is stated (the masses are decreased in simulations 5 and 6). The planets orbit the barycentre of the −1 system, which is not centred on the star as a result of the high planet mass. This means that the planetary orbits have a low ini- −1:5 tial eccentricity as they are initiated on orbits circular around the star. The initial orbital eccentricities vary between different sys- −2 tems as the inclinations, longitude of ascending nodes, and true 2 1.5 1 0.5 0 −0:5 −1 −1:5 −2 anomalies are randomised. East ["] We vary the separation between the initial planet orbits (re- garding the planets as test particles) in terms of the mutual Hill Fig. 1. Observations of the HR 8799 planets. The black dashed line radius, which is defined as follows: corresponds to the position angle of the inclination as estimated by !1=3 Matthews et al.(2014) with the 1σ uncertainty shown by the grey rp1 + rp2 Mp1 + Mp2 ± RH = ; (1) region. 2 3M? when integrating the orbits of the planets, assumed initially cir- where r signifies star-planet separation in the orbital plane and M cular, seen pole-on and non-resonant (Fabrycky & Murray-Clay mass (Chambers et al.
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